Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Invariant measures for piesewise fractional linear maps

Fritz Schweiger

Abstract

The first part deals with piecewise fractional linear maps with three branches. Given a map $T$ a map $S$ is called a related map if some branches of $T$ are replaced by a 'flipped' branch, namely a branch of $1-T$. The main question is if $T$ and $S$ have a common invariant measure. The short second part presents invariant measures of a new type.

Invariant measures for piesewise fractional linear maps

Abstract

The first part deals with piecewise fractional linear maps with three branches. Given a map a map is called a related map if some branches of are replaced by a 'flipped' branch, namely a branch of . The main question is if and have a common invariant measure. The short second part presents invariant measures of a new type.
Paper Structure (5 sections, 4 theorems, 53 equations)

This paper contains 5 sections, 4 theorems, 53 equations.

Table of Contents

  1. 0. Introduction
  2. 1. Related maps with one 'flip'
  3. 2. Related maps with two 'flips'
  4. 3. Related maps with three 'flips'
  5. 4. New measures through the back door

Key Result

Theorem 1

(1) The maps $T$ and $S_1$ both have a natural dual and the same invariant measure if the conditions and are satisfied. (2) The maps $T$ and $S_2$ both have a natural dual and the same invariant measure if the conditions and are satisfied. (3) The maps $T$ and $S_3$ both have a natural dual and the same invariant measure if the conditions and are satisfied.

Theorems & Definitions (14)

  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Theorem 3
  • proof
  • Theorem 4
  • proof
  • Example 1
  • Example 2
  • ...and 4 more